<p>In this paper, we study the hazard rate by a semiparametric model with an unspecified functional form and involving an index structure. We propose a random censored local linear kernel-weighted least squares estimator for the nonparametric component, treating it as a bivariate function, and this estimator enjoys uniform consistency. The induced profile likelihood estimator of the index coefficient vector achieves the information lower bound. This semiparametric efficient result inspires the construction of a class of efficient estimating equations. For computational feasibility, another two sets of estimating equations are presented based on double robustness. The efficient estimation can be readily implemented by an adapted Newton-Raphson algorithm. Asymptotic properties of all estimators are rigorously established and derived. Numerical results validate the performance of the proposed estimators.</p>